Catalog sales companies such as L.L. Bean encourage customers to place orders by mailing seasonal catalogs to prior customers. The expected profit from each mailed catalog can be expressed as the product
Expected profit = p × D × S
where p is the probability that the customer places an order, D is the dollar amount of the order, and S is the percentage profit earned on the total value of an order. Typically 10% of customers who receive a catalog place orders that average $125, and 20% of that amount is profit.
(a) What is the expected profit under these conditions?
(b) The response rates and amounts are sample estimates. If it costs the company $2.00 to mail each catalog, how accurate does the estimate of p need to be in order to convince you that the next mailing is going to be profitable?